79.1.4 problem 1 (iv)

Internal problem ID [18491]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 1 (iv)
Date solved : Tuesday, January 28, 2025 at 11:50:50 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 15

dsolve([diff(x(t),t)=1/sqrt(1+t^2),x(1) = 0],x(t), singsol=all)
 

\[ x = \operatorname {arcsinh}\left (t \right )-\ln \left (1+\sqrt {2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 12

DSolve[{D[x[t],t]==1/Sqrt[1+t^2],{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \text {arcsinh}(t)-\text {arcsinh}(1) \]